Synopsis

The accurate characterization of diffusion process with MRI is compromised by various artefacts including intensity related errors. If not appropriately accounted for, model estimates can become significantly biased resulting in erroneous metrics. Slicewise intensity errors, in particular, are often handled by excluding the entire image or slice information, or by voxelwise robust estimators that experience difficulties in partial volume regions. In this work, we describe a fast and accurate algorithm to detect slicewise outliers and a framework to incorporate this information as data uncertainty in model estimation algorithms.

Introduction

Slicewise intensity artefacts arising from subject motion or hardware issues can impede the accurate characterization of diffusion with MRI^1–4. When not appropriately accounted for, these intensity errors can significantly confound quantitative studies with groups and individuals, and the importance of this problem was once again stressed by recent work^5,6. Robust voxelwise estimators are suboptimal to detect slicewise errors, especially when the outlier becomes distributed across multiple slices during the motion correction^7–10. Available slicewise detection methods often exclude entire DWIs¹¹ or individual slices^5,12–15, which can lead to the unnecessary loss of good data as well as numerical issues¹⁶.

We present an automated and fast tool to detect slicewise outliers in multishell dMRI data prior to motion corrections. The framework, coined SOLID (Slicewise OutLIer Detection), naturally incorporates this information as data uncertainty in model estimation. SOLID is based on a straightforward slicewise intensity metric and does not rely on modeling or signal prediction, thereby lifting constraints set on the acquisition protocol by other algorithms⁵. As the SOLID-informed estimation downweights outliers instead of excluding them, it promotes that the mathematical problem remains well-conditioned and supports the convergence of iterative estimation algorithms¹⁷.

SOLID was evaluated using comprehensive diffusion and kurtosis tensor simulations, compared to previously published tools⁵, and finally validated with dMRI data from 54 newborn subjects in which slicewise outliers were manually labelled.

Methods

Slicewise outlier detection prior to motion correction:

The SOLID framework is visualized in Figure 1. Outlier detection is based on a slicewise intensity metric $$$y_{k,l}$$$ (e.g. variance) calculated from all brain voxels within each slice $$${k}$$$ and DWI $$${l}$$$. Slicewise modified Z-scores¹⁸ $$$\zeta_{k,l}$$$ are obtained by computing the median $$$\tilde{y}_{k}$$$ and median absolute deviation $$$\textrm{MAD}_{k}$$$⁷ (eq.1) across all DWIs (eq.2):

$$\textrm{MAD}_k=1.4826\cdot(|y_{k,l}-\tilde{y}_k|),\tag{1}$$

$$\zeta_{k,l}=\frac{{y_{k,l}-\tilde{y}_k}}{{\textrm{MAD}_k}}.\tag{2}$$

Informed model-estimation after motion correction:

Voxelwise interpolated modified Z-scores are calculated by applying the transformation obtained from motion correction for each DWI $$$\mathbf{T}_{l}(\mathbf{x})$$$ to each corresponding modified Z-score volume $$$\xi_{l}$$$ created from the slicewise modified Z-scores $$$\xi_{k,l}$$$; i.e. $$$\xi_{l}^{'}(\mathbf{x}^{'})=\xi_{l}(\mathbf{T}_{l}(\mathbf{x})))$$$. Subsequently, SOLID weights $$$S_{l}(\mathbf{x}^{'})$$$ between 0 and 1 - representing data uncertainty estimates - are obtained by eq.3:

$$S_{l}(\mathbf{x}^{'})=\left\{\begin{array}{l} 0,\quad if \ \xi_{l}^{'}(\mathbf{x}^{'})>t_{Upper} \\1,\quad if \ \xi_{l}^{'}(\mathbf{x}^{'})<t_{Lower}\\\frac{\xi_{l}^{'}(\mathbf{x}^{'})-t_{Upper}}{t_{Upper}-t_{Lower}},\quad otherwise\end{array}\right. .\tag{3}$$

Modified Z-scores below the lower threshold (suggested $$$t_{Lower}=3.5$$$) are considered normal and have a weight of 1 during model estimation, modified Z-scores above the upper threshold (suggested $$$t_{Upper}=10$$$) are excluded as outliers, and intermediate values get linearly downweighted.

Evaluation:

Firstly, outlier detection was evaluated using six sets of 1000 full-brain DWI simulations based on diffusion- and kurtosis tensors obtained from the MASSIVE database¹⁸. Each set consisted of 30 DWIs on two shells with b-values 1000s/mm² and 2000s/mm², from which eight were replaced with artefactual DWIs having five outlier slices each. Rician noise was introduced with multiple signal-to-noise ratios (SNR). Secondly, SOLID was compared to FSL’s slicewise outlier detection included in EDDY⁵. Finally, SOLID was validated using manually labeled slicewise outliers from 54 neonatal subjects.

Results & Discussion

Figure 2 shows SOLID receiver-operating-characteristic (ROC) curves for various outlier simulation setups with multiple SNRs. SOLID had a good performance in all simulations as indicated with the lowest recorded area-under-curve (AUC) value of 0.94.

Figure 3 shows a comparison between SOLID and FSL EDDY ROC curves: SOLID overall achieved similar specificity and higher sensitivity compared to EDDY, likely due to the minimum number of voxels per slice required by EDDY.

Figure 4 shows an evaluation of four different slicewise metrics on manually labelled outlier slices in the neonatal dataset, advocating the choice of variance or mean.

Conclusion

Acknowledgements

References

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